Expectation and variance of item resemblance distributions in a convolution-correlation model of distributed memory

The present paper extends the applicability of distributed memory models that use convolution and correlation as their encoding and retrieval operations by providing analytic derivations of the expressions needed to apply such models to a wide range of experimental paradigms. These extensions allow such models to predict recall and recognition performance for single items and double and triple associations under optimal storage and retrieval conditions as well as in situations of degraded probe information at time of test or incomplete encoding of information at time of study. Part I gives a brief review of one convolution-correlation memory model, TODAM (Murdock (1982). Psychological Review, 89, 609-626; TODAM (Murdock (1983). Psychological Review, 90, 316-338). Part II provides the derivations for expectations and variances of the distributions of dot-product resemblance between an extensive list of memory vectors and probe vectors. Expressions of the first two moments of such resemblance distributions in terms of the model parameters are needed to derive model predictions for such dependent measures as recall or recognition accuracy or d′. Part III illustrates the use these resemblance distribution moments by deriving predictions for the data of three experimental paradigms: (1) recall with partial cues (Tulving & Watkins (1973). American Journal of Psychology, 86, 739-748), (2) recognition of rapidly presented information (Loftus, (1974). Memory and Cognition, 2, 545-548), and (3) recognition in context of a triple association learning task (Clark & Shiffrin (1987). Memory and Cognition, 15, 367-378).